A particle moves on a circle with angular speed ω = 2t². At t = 1 s, the net acceleration makes an angle φ with the inward radial direction. If tanφ = N, find N.
Physics · Circular Motion · kinematics of circular motion
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Question

A particle moves on a circle with angular speed ω = 2t². At t = 1 s, the net acceleration makes an angle φ with the inward radial direction. If tanφ = N, find N.

G1 Physics · Accepted Answer

At t=1 s, ω=2 rad/s and α=dω/dt=4t=4 rad/s². With φ measured from the inward radial direction, tanφ=aₜ/a_c=(Rα)/(Rω²)=α/ω²=4/4=1. Hence N=1.